Maths IES Brain Teaser

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Maths IES Brain Teaser

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A thief is running after stealing two gold bars from an ancient and sacred temple. The villagers see him running and runs after him. While running, he comes across a rope bridge. There is a warning board on the start of the bridge stating that the rope can only accommodate a weight of 130 pounds.

Now the thief weighs 100 pounds and the gold bars weigh 20 pounds each. But ignoring the warning he just crosses the bridge with both gold bars. He manages to cross safely. How?

You must be aware of the fact that the standard weighing system is Imperial system. This is how we weigh things or ourselves and thus the warning must be for 130 pounds according to the Imperial system.

But gold is weighed in the Troy system. In Troy system, 12 ounces makes one pound whereas in Imperial system, 16 ounces make one pound.

Thus 40 pounds (20+20) of gold bars will be 30 pounds in imperial system. The weight of thief is 100 pounds. Thus, the total is 130 pounds which can be accommodated on the rope and thus he was able to cross safely.

Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.
Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.

A man of faith visits the holy land where three temple are erected in a row offering a surreal divinity to the place. Awestruck at the sight of the magnificent temples, he visits the first temple where he finds that the number of flowers in his basket increases to double the number as soon as he sets his foot inside the temple. Astonished by the miracle he is completely happy and seeks it as a blessing of his god. He offers a few flowers to the stone idol of god and moves out.

Then he visits the second temple, where the same miracle happens again. The number of flowers in his basket again double up in number. With a smile on his face, he offers a few of flowers to the stone idol again and walks out after praying.

The moment he enters the third temple, the number of flowers increases to double again. Now he feels entirely blessed. He offers all the flowers at the feet of the stone idol and walks out in a moment of bliss.

When he walks out, he has no remaining flowers with him. He offered equal number of flowers at each of the temple. What is the minimum number of flowers he had before entering the first temple? How many flowers did he offer at each temple?

Let m be initial number of flowers and n be the flowers offered at each temple by the man.
Initial flowers = m
After stepping into the first temple = 2m
Flowers offered at the first temple = n
Remaining flowers = 2m – n

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?

Day One: You make your first cut at the 1/7th mark and give that to the worker.
Day Two: You cut 2/7ths and pay that to the worker and receive the original 1/7th in change.
Day three: You give the worker the 1/7th you received as change on the previous day.
Day four: You give the worker 4/7ths and he returns his 1/7th cut and his 2/7th cut as change.
Day Five: You give the worker back the 1/7th cut of gold.
Day Six: You give the worker the 2/7th cut and receive the 1/7th cut back in change.
Day Seven: You pay the worker his final 1/7th.

Suppose there is a Christmas tree and four angels are sitting on it amidst the other ornaments. Two of them have black halos and two of them have white halos. No body among them can see above their head. Angel A is sitting on the top branch and can see angels B and C sitting below him. B can see C who is sitting in a branch lower than his. Angel D is at the base of the tree and can't be seen due to the branches in between. Also, he can't see anybody as well.

If they are asked to guess the color of their own halo (they dont know that), who do you think will be able to deduce and speak up first with a right answer?

Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.

David and Albert are playing a game. There are digits from 1 to 9. The catch is that each one of them has to cut one digit and add it to his respective sum. The one who is able to obtain a sum of exact 15 will win the game?

You are a friend of David. Do you suggest him to play first or second?

Explanation:
Let's suppose that David plays first and he picks 9. Then Albert will definitely pick 8. Now, David will have to pick 7 or Albert will pick 7 in his turn. But if David picks up 7, then he will score 16 that is beyond 15 and will lose. So one thing is for sure, no one will be willing to start with the highest digits.

Suppose David plays first and picks up 1, Albert will pick 2. Then David will pick 3 and Albert will pick 4. Now David will be forced to pick 9. The score is 6 to 13 and thus David will have no chance of winning.

If David Picks 9 after Albert has picked up 2, then Albert will pick 8 and the score will become 10 to 10. Thus David will pick 3 as picking 7 will send him past 15. Now Albert will pick 4 and David has nothing to pick for winning. Thus Albert wins.